# Rule base and adaptive fuzzy operators cooperative learning of Mamdani fuzzy systems with multi-objective genetic algorithms

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## Abstract

In this paper, we present an evolutionary multi-objective learning model achieving cooperation between the rule base and the adaptive fuzzy operators of the inference system in order to obtain simpler, more compact and still accurate linguistic fuzzy models by learning fuzzy inference adaptive operators together with rules. The multi-objective evolutionary algorithm proposed generates a set of fuzzy rule based systems with different trade-offs between interpretability and accuracy, allowing the designers to select the one that involves the most suitable balance for the desired application. We develop an experimental study testing our approach with some variants on nine real-world regression datasets finding the advantages of cooperative compared to sequential models, as well as multi-objective compared with single-objective models. The study is elaborated comparing different approaches by applying non-parametric statistical tests for pair-wise. Results confirm the usefulness of the proposed approach.

## Keywords

Linguistic fuzzy modelling Interpretability-accuracy trade-off Multi-objective genetic algorithms Adaptive inference system Adaptive defuzzification Rule learning## Notes

### Acknowledgments

Paper supported in part by the Spanish Ministry of Education and Science under grant no. TIN2008-06681-C06-06, and the Andalusian government under grant no. P07-TIC-03179.

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